On reciprocal and reverse Balaban indices - Zhou, Bo (Array, 2009)
Summary: The Ivanciuc-Balaban operator of a graph G is defined [see full text for definition] where M is its molecular matrix with positive row-sums, m is the number of edges, µ is the cyclomatic number, Mi is the i-th row sum of M and the summation goes over all edges from the edge-set E(G). Here we consider the reciprocal Balaban index rJ(G)=J(RD, G) and the reverse Balaban index rJr(G)=J(RW, G), where RD and RW are respectively the reciprocal distance matrix and the reverse Wiener matrix of G. Various lower and upper bounds for these two types of Balaban-like indices are reported